Question

The approximate value of (1.0002)³⁰⁰⁰ is.

• A. 1.6
• B. 1.4
• C. 1.8
• D. 1.2

Answer 1

Answer: (A)

1.6

Answer 2

$\frac{(1 + x)^{3/2} - \left( 1 + \frac{1}{2}x \right)^{3}}{(1 - x)^{1/2}}$

$\frac{1 + \frac{3}{2}x + \frac{\frac{3}{2}.\frac{1}{2}}{2}x^{2} - \left( 1 + \frac{3x}{2} + \frac{3.2}{2}\frac{x^{2}}{4} \right)}{(1 - x)^{1/2}}$ $\frac { ( 3000 ) ( 2999 ) ( 2998 ) } { 1.2 .3 } ( 0.0002 ) ^ { 3 } +$

We want to get answer correct to only one decimal places and as such we have left further expansion.

= $\frac{- \frac{3}{8}x^{2}}{(1 - x)^{1/2}}$ = 1.6